Some problem statements in decision theory can be non universal. Like, they are possible as situations that can happen, but they are invalid as problems to ask what would you do in them.
Suppose Omega gives a single box with $100 to people who don't say banana after seeing the explanation of the setup and the box. You encounter such situation. Would you say "banana"?
Like, it's funky premise? It's not applicable to all people? It would not give me such opportunity, so the premise is invalid.
It pre selects what kind of guys get to participate. So, some guys don't. So, if you ask what those guys will do in that situation? It has invalid premise of them being in selection.
This problem conditions on you having particular policy or one of the subset of policies.
You can straightforwardly correct some such confused statements, by saying what happens when you are not in selection.
Newcomb's problem is fine on that front, it accommodates every kind of strategy, namely, "see opaque and transparent boxes" -> two box, and "see opaque and transparent boxes" -> one box.
Transparent Newcomb's problem needs adjustment for this selection effect danger, because in that case you can go against the prediction, e.g. "take $0 box if only one is full and two box if they both are full". What Omega offers to those guys, huh? No matter what Omega does, they always go against prediction.
One solution is "Omega leaves both full IFF you one box after seeing both full", then some contrarians do receive only $1000 and leave with $0 after one boxing. Another "Omega leaves both full IFF no matter what you see you take one" -- but this one is closer to counterfactual mugging.
Smoker's lesion might be one such problematic problem. Agents will act on correlation they perceive, but in doing so, destroy the correlation. You can fix this by introducing staged information gain, like "People decided to collect the statistic each 10 years. This was the first time they did that. There is such correlation. Before next statistic collection, what do you do? " or selection effects, like "even after acting on this correlation, correlation remains" -- and this looks like it makes weird postulates, that might be non universal.
XOR blackmail uses this selection effect deliberately. There is a selection effect to what kind of agents the letters arrives. If you received the letter, then you have termites XOR you will pay small fee. But it's evidence about the state of the world not your decision, if you are the kind of person who would not pay. There is no way to act on this information and get out of bounds of what is postulated.
Ways to resolve problems with how such questions are posed:
You can explicitly say what happens if you are not in selection. E.g.
Banana problem with selection:
Omega takes a look at you from stealth. If it thinks you would not say banana if given $100 and explanation of the setup, it approaches you and does it. Otherwise it leaves without turning off stealth or explaining anything.
Then everyone is in selection again.
I think XOR blackmail problem is of this type already. Smoker's lesion deals with this incorrectly / underdefined. Transparent boxes Newcomb's can be fixed in the same way. Although I think the one fixed with counterfactual predictor is better as a problem, closer to original Newcomb's.
E.g. Transparent boxes Newcomb's with selection:
Omega takes a look at you from stealth. If it thinks that "you would two box if given $1000" XOR "you would one box if given $1m + $1000" is True, then it gives you the boxes from the consistent scenario and explains the setup. If that statement with XOR is false, it leaves without turning off stealth or explaining anything.
(both EDT and CDT get approached and given only $1000, as they don't one box if boxes are full and two box if only one is full. Contrarians don't get approached)
Transparent boxes Newcomb's with counterfactual prediction version1:
Omega leaves both full IFF you one box conditional on seeing both full, otherwise it fills only $1k box.
(some people would receive $0 + $1000 and take $0 box. Contrarians, you know.)
Version2:
Omega leaves both full IFF no matter what you see you take one, otherwise it fills only $1k box.
Smoker's lesion, staged information gain:
People decided to collect the statistic each 10 years. This was the first time they did that. There is correlation of smoking with cancer. Moreover it was discovered that the correlation is through the lesion entirely. You can't observe the lesion in yourself or compare how strongly you want to smoke with other people, e.g. it's hard to interpret your own state with your amount of resources. Before next statistic collection, what do you do?
(CDT smokes extra hard, EDT stops smoking. Next statistic collection correlation vanishes, EDT starts to smoke too.)
Some problem statements in decision theory can be non universal. Like, they are possible as situations that can happen, but they are invalid as problems to ask what would you do in them.
Like, it's funky premise? It's not applicable to all people? It would not give me such opportunity, so the premise is invalid.
It pre selects what kind of guys get to participate. So, some guys don't. So, if you ask what those guys will do in that situation? It has invalid premise of them being in selection.
This problem conditions on you having particular policy or one of the subset of policies.
You can straightforwardly correct some such confused statements, by saying what happens when you are not in selection.
Newcomb's problem is fine on that front, it accommodates every kind of strategy, namely, "see opaque and transparent boxes" -> two box, and "see opaque and transparent boxes" -> one box.
Transparent Newcomb's problem needs adjustment for this selection effect danger, because in that case you can go against the prediction, e.g. "take $0 box if only one is full and two box if they both are full". What Omega offers to those guys, huh? No matter what Omega does, they always go against prediction.
One solution is "Omega leaves both full IFF you one box after seeing both full", then some contrarians do receive only $1000 and leave with $0 after one boxing. Another "Omega leaves both full IFF no matter what you see you take one" -- but this one is closer to counterfactual mugging.
Smoker's lesion might be one such problematic problem. Agents will act on correlation they perceive, but in doing so, destroy the correlation. You can fix this by introducing staged information gain, like "People decided to collect the statistic each 10 years. This was the first time they did that. There is such correlation. Before next statistic collection, what do you do? " or selection effects, like "even after acting on this correlation, correlation remains" -- and this looks like it makes weird postulates, that might be non universal.
XOR blackmail uses this selection effect deliberately. There is a selection effect to what kind of agents the letters arrives. If you received the letter, then you have termites XOR you will pay small fee. But it's evidence about the state of the world not your decision, if you are the kind of person who would not pay. There is no way to act on this information and get out of bounds of what is postulated.
Ways to resolve problems with how such questions are posed:
You can explicitly say what happens if you are not in selection. E.g.
Banana problem with selection:
Then everyone is in selection again.
I think XOR blackmail problem is of this type already. Smoker's lesion deals with this incorrectly / underdefined. Transparent boxes Newcomb's can be fixed in the same way. Although I think the one fixed with counterfactual predictor is better as a problem, closer to original Newcomb's.
E.g. Transparent boxes Newcomb's with selection:
(both EDT and CDT get approached and given only $1000, as they don't one box if boxes are full and two box if only one is full. Contrarians don't get approached)
Transparent boxes Newcomb's with counterfactual prediction version1:
(some people would receive $0 + $1000 and take $0 box. Contrarians, you know.)
Version2:
Smoker's lesion, staged information gain:
(CDT smokes extra hard, EDT stops smoking. Next statistic collection correlation vanishes, EDT starts to smoke too.)
I'm not sure how to pose it with selection.